---
title: "Newton's Second Law: Force, Mass and Acceleration"
description: "A resultant force gives an acceleration in its own direction, with F = ma. Weight is mass times g, which is why objects of different mass fall together."
canonical: https://lightmysky.com/learn/mathematics/newtons-second-law-force-mass-and-acceleration-mt_SKO85AcKdb
source: https://lightmysky.com/learn/mathematics/newtons-second-law-force-mass-and-acceleration-mt_SKO85AcKdb.md
retrieved: 2026-09-12
---

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# Newton's Second Law: Force, Mass and Acceleration

A resultant force gives an acceleration in its own direction, with F = ma. Weight is mass times g, which is why objects of different mass fall together.

Subject: Mathematics · Area: Mechanics · Ages 17 to 18
Page: https://lightmysky.com/learn/mathematics/newtons-second-law-force-mass-and-acceleration-mt_SKO85AcKdb

## Ready when they can

- Find the acceleration of a 2 kg object under a 6 N resultant force
- Keep mass and weight apart, with the right units for each
- Find the resultant force needed to slow a moving object at a stated rate

## Lesson: Push, mass and how fast it picks up

Resultant force equals mass times acceleration: F = ma. A 2 kg object under a 6 N resultant accelerates at 6 over 2 = 3 m/s squared. Mass resists: the same force on double the mass gives half the acceleration.

**Example.** A 5 kg trolley accelerating at 2 m/s squared needs F = 5 times 2 = 10 N driving it. The law works for slowing too: a 1000 kg car braking at 2 m/s squared feels 1000 times 2 = 2000 N against its motion.

Mass counts matter in kilograms and stays the same everywhere, while weight is gravity pulling on it in newtons. On Earth with g = 10 N/kg, a 5 kg bag of food weighs 5 times 10 = 50 N. A 2 kg bag weighs 20 N, never 2 N.

**Tip.** Weight is mass times g, and F = ma divides it straight back out: a = mg over m = g. That is why a 2 kg and a 5 kg object fall with the same acceleration. Bigger weight, same extra mass to move, same g.

**Recap.** Resultant force makes mass accelerate by F = ma, and weight is just mass times g.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Modelling Motion in a Straight Line](https://lightmysky.com/learn/mathematics/modelling-motion-in-a-straight-line-mt_no78_6w1rS)

## Opens up

- [Friction and the Coefficient of Friction](https://lightmysky.com/learn/mathematics/friction-and-the-coefficient-of-friction-mt_EwFUd9N24W)
- [Newton's Second Law as a Differential Equation](https://lightmysky.com/learn/science/newtons-second-law-as-a-differential-equation-mt_LzSNSkEovH)
- [Newton's Second Law in Two Dimensions](https://lightmysky.com/learn/mathematics/newtons-second-law-in-two-dimensions-mt_yNUFF3lxlj)